I have seen this several times.
Some dogs have very sensitive skin that can react to the metal type on the prongs of the collars that is used in making the collars. This is similar to a person who has an allergy to nickel plated jewelry. Some dogs are also just sensitive to the motion of the collar on the neck as well - just the rubbing of it up and down can cause irritation.
I think you are on the right track - discontinue the collar use, keep the wounds clean and start antbiotics. In my opinion, both dogs should be on antibiotics, but for sure the one with the more severe wound. The antibiotic treatment should be continued for at least 10 days or until the wounds are closed. You may need to get more antibiotics from your vet.
Good luck with your dogs!
Dr. Tanis!
Dog Veterinarian
10 years experience in small animal emergency medicine
Thank you! I think I will call my vet in the AM to get more anitbiotics for our older one as well. I was just worried that the collar was continually shocking them and this caused the rash. When we removed the collar from our younger boxer the prongs were slimy.